I placed a couple of my wife’s white salad plates in my smoker under the coke-can-chickens the last time I smoked to help stabilize the can on the grill. When I removed the plates they were black and looked horribly burnt. I used oven cleaner and a little elbow grease and they came clean. Got photos but haven't posted yet.

A casserole should be cooked using indirect heat. Propane burns clean so if you’re not smoking it, you should have very little worry about discoloration.

Even though you will be cooking this with indirect heat on a gas grill unless you have very good control of the heat I would not chance a glass caserole dish even if it is oven safe. I think that with the close proximity of the heat temps could still get high enough to break it. I have used dispsoable aluminum pans for caseroles on a grill with very good success. I would suggest you use these instead. Added bonus, you don't have to clean them.

I do all my baking during the summer months in my gas grill. After all, the grill is nothing but an outdoor oven. The temp remains constant and the cavity is big enough to handle any baking dish. As mentioned above, gas grills don’t give out much smoke (when the inside is clean), and therefore they’re suitable for baking. Don’t miss understand me, I like smoke flavor as much as anyone, but not on all desserts. I’ve used a verity of baking dishes in the process to include glass; I’ve never had any problems with them. The only thing you have to watch out for is when baking casseroles with cheese used as topping, you must cover the dish with foil for the majority of cooking time. For some reason, the cheese browns too fast and burns quickly when baking inside of a grill. I always bake my mac&cheese and scallop potatoes inside my gas grill; they always turn out very well. And the smoke flavor goes well with these dishes, so a charcoal grill will work just as well.
Good Luck.